Name: FAD 1013
Uploaded: 2023-10-06
Duration: 5 min 24 s
Description: FAD 1013. INDICES, SURDS AND LOGARITHMS WEEK 1 (L2 & L3) Sir JEDZRY.

FAD 1013. INDICES, SURDS AND LOGARITHMS WEEK 1 (L2 & L3) Sir JEDZRY. 

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INDICES, SURDS AND LOGARITHMS WEEK 1 (L2 & L3) Sir JEDZRY

“exponent” or “index” (plural “indices”). “Base”. 

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“exponent” or “index” 
(plural “indices”)

We say this as “3 to the power of 4” or “3 raised to the power of 4” or “3 to the 4”.

The exponent tells us how many times the base appears in a product.

5 appears 2 times.. It is possible for the exponent to be fractional, 0 or negative.. 

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When the exponent (index) is a positive integer, indicates how many times the base is repeated in the multiplication.

It is possible for the exponent to be fractional, 0 or negative.

4. INDICES: Rules/Properties. abstract. abstract. 

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Simplify the following.. 1. Questions on provided worksheet.. 

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Introduction to exponent. A black text with a white background Description automatically generated. 

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A black text with a white background

Description automatically generated

Rational roots. -3 is the 5th root of -243 since (-3)5 =-243.. 

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-3 is the 5th root of -243 since (-3)5 =-243.

nth root – For any real number a, b, and positive integer n, if an = b, then “a is the nth root of b”.

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[Audio] Remind students of the general form of each result where a is any number and m and n are integers.. 

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Here is a summary of the index laws for all rational exponents:

11. SURDS. radical symbo radicand 2 index—O radical. 

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radical symbo
radicand
2
index—O
radical

12. Properties of nth Roots Property = a if n is odd a I if n is even Example 16 2 3 (-5)3 = -5. 

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Properties of nth Roots
Property
= a if n is odd
a I if n is even
Example
16 2
3 (-5)3 = -5

When simplifying expression related to surds, make sure to rationalise the denominator => get rid of the radical sign in the denominator.. 

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When simplifying expression related to surds, make sure to rationalise the denominator => get rid of the radical sign in the denominator.

EXAMPLE 3. Rationalize the following expressions.. 

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Log of x to the base a is y. abstract. Note: log of negatives and zero are not Defined in Reals. 

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Note: log of negatives and zero are not Defined in Reals

Laws of Logarithms. PROPERTIES OF LOGARITHMS. abstract. 

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SOLVING RADICAL EQUATIONS. How to solve: Leave one of the terms with surd on one side and all other terms on the other. Square both sides of the equation and simplify. Repeat step 1 and step 2 if there is more than one term with surd (until all the surds are removed). Check the solution (true solutions of the original equation). Values which do not satisfy the equation = extraneous solutions (not a valid solution).. 

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How to solve: Leave one of the terms with surd on one side and all other terms on the other. Square both sides of the equation and simplify. Repeat step 1 and step 2 if there is more than one term with surd (until all the surds are removed). Check the solution (true solutions of the original equation). Values which do not satisfy the equation = extraneous solutions (not a valid solution).

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SOLVING LOGARITHMIC EQUATIONS. The properties of log are used to simplify and solve the equations.. 

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The properties of log are used to simplify and solve the equations.

Each solution must be checked, and extraneous solutions are discarded.

Logarithms are not defined for negative numbers.

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Reminder !!!!. Quadratic Equation is an equation with maximum degree of variable 2.. 

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Quadratic Equation is an equation with maximum degree of variable 2.

Please don’t forget to watch my videos in Spectrum

33. _ ællAlyavad&21u P,iyanæ? ')tJZö. 

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FAD 1013

Remind students of the general form of each result where a is any number and m and n are integers.